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Teoriya Veroyatnostei i ee Primeneniya, 1978, Volume 23, Issue 1, Pages 161–169 (Mi tvp3021)  

This article is cited in 12 scientific papers (total in 12 papers)

Short Communications

The recurrency of oscillating random walks

B. A. Rogozin, S. G. Foss

Novosibirsk
Abstract: Let $Y=\{y_n\}_{n=0}^{\infty}$ be an oscillating random walk ([1]):
$$ y_0=0,\qquad y_{n+1}-y_n= \begin{cases} \xi'_{n+1},&y_n\le 0,\\ \xi''_{n+1},&y_n>0, \end{cases} \qquad(n=1,2,\dots), $$
$\{\xi'_n\}_{n=1}^{\infty}$ and $\{\xi''_n\}_{n=1}^{\infty}$ be two sequences of independent identically distributed, in each sequence, random variables with values in the set $\{0,\pm 1,\pm 2,\dots\}$,
\begin{gather*} S'_0=S''_0=0,\\ S'_n=\sum_{k=1}^n\xi'_k,\qquad S''_n=\sum_{k=1}^n\xi''_k,\qquad n=1,2,\dots \end{gather*}
The random walks $S'_n=\{S'_n\}_{n=0}^{\infty}$ and $S''_n=\{S''_n\}_{n=0}^{\infty}$ are aperiodic. It is shown that $Y$ can be transient in the case $\mathbf M\xi'_1=\mathbf M\xi''_1=0$. A recurrency condition for $Y$ is obtained when $S'$ and $S''$ are stable random walks.
Received: 09.06.1976
English version:
Theory of Probability and its Applications, 1978, Volume 23, Issue 1, Pages 155–162
DOI: https://doi.org/10.1137/1123015
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. A. Rogozin, S. G. Foss, “The recurrency of oscillating random walks”, Teor. Veroyatnost. i Primenen., 23:1 (1978), 161–169; Theory Probab. Appl., 23:1 (1978), 155–162
Citation in format AMSBIB
\Bibitem{RogFos78}
\by B.~A.~Rogozin, S.~G.~Foss
\paper The recurrency of oscillating random walks
\jour Teor. Veroyatnost. i Primenen.
\yr 1978
\vol 23
\issue 1
\pages 161--169
\mathnet{http://mi.mathnet.ru/tvp3021}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=494508}
\zmath{https://zbmath.org/?q=an:0423.60059|0382.60076}
\transl
\jour Theory Probab. Appl.
\yr 1978
\vol 23
\issue 1
\pages 155--162
\crossref{https://doi.org/10.1137/1123015}
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  • https://www.mathnet.ru/eng/tvp/v23/i1/p161
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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